A Few Photons Among Many: Unmixing Signal and Noise for Photon-Efficient Active Imaging

Conventional LIDAR systems require hundreds or thousands of photon detections to form accurate depth and reflectivity images. Recent photon-efficient computational imaging methods are remarkably effective with only 1.0 to 3.0 detected photons per pixel, but they are not demonstrated at signal-to-background ratio (SBR) below 1.0 because their imaging accuracies degrade significantly in the presence of high background noise. We introduce a new approach to depth and reflectivity estimation that focuses on unmixing contributions from signal and noise sources. At each pixel in an image, short-duration range gates are adaptively determined and applied to remove detections likely to be due to noise. For pixels with too few detections to perform this censoring accurately, we borrow data from neighboring pixels to improve depth estimates, where the neighborhood formation is also adaptive to scene content. Algorithm performance is demonstrated on experimental data at varying levels of noise. Results show improved performance of both reflectivity and depth estimates over state-of-the-art methods, especially at low signal-to-background ratios. In particular, accurate imaging is demonstrated with SBR as low as 0.04. This validation of a photon-efficient, noise-tolerant method demonstrates the viability of rapid, long-range, and low-power LIDAR imaging

Probabilistic modeling for single-photon lidar

Lidar is an increasingly prevalent technology for depth sensing, with applications including scientific measurement and autonomous navigation systems. While conventional systems require hundreds or thousands of photon detections per pixel to form accurate depth and reflectivity images, recent results for single-photon lidar (SPL) systems using single-photon avalanche diode (SPAD) detectors have shown accurate images formed from as little as one photon detection per pixel, even when half of those detections are due to uninformative ambient light. The keys to such photon-efficient image formation are two-fold: (i) a precise model of the probability distribution of photon detection times, and (ii) prior beliefs about the structure of natural scenes. Reducing the number of photons needed for accurate image formation enables faster, farther, and safer acquisition. Still, such photon-efficient systems are often limited to laboratory conditions more favorable than the real-world settings in which they would be deployed. This thesis focuses on expanding the photon detection time models to address challenging imaging scenarios and the effects of non-ideal acquisition equipment. The processing derived from these enhanced models, sometimes modified jointly with the acquisition hardware, surpasses the performance of state-of-the-art photon counting systems. We first address the problem of high levels of ambient light, which causes traditional depth and reflectivity estimators to fail. We achieve robustness to strong ambient light through a rigorously derived window-based censoring method that separates signal and background light detections. Spatial correlations both within and between depth and reflectivity images are encoded in superpixel constructions, which fill in holes caused by the censoring. Accurate depth and reflectivity images can then be formed with an average of 2 signal photons and 50 background photons per pixel, outperforming methods previously demonstrated at a signal-to-background ratio of 1. We next approach the problem of coarse temporal resolution for photon detection time measurements, which limits the precision of depth estimates. To achieve sub-bin depth precision, we propose a subtractively-dithered lidar implementation, which uses changing synchronization delays to shift the time-quantization bin edges. We examine the generic noise model resulting from dithering Gaussian-distributed signals and introduce a generalized Gaussian approximation to the noise distribution and simple order statistics-based depth estimators that take advantage of this model. Additional analysis of the generalized Gaussian approximation yields rules of thumb for determining when and how to apply dither to quantized measurements. We implement a dithered SPL system and propose a modification for non-Gaussian pulse shapes that outperforms the Gaussian assumption in practical experiments. The resulting dithered-lidar architecture could be used to design SPAD array detectors that can form precise depth estimates despite relaxed temporal quantization constraints. Finally, SPAD dead time effects have been considered a major limitation for fast data acquisition in SPL, since a commonly adopted approach for dead time mitigation is to operate in the low-flux regime where dead time effects can be ignored. We show that the empirical distribution of detection times converges to the stationary distribution of a Markov chain and demonstrate improvements in depth estimation and histogram correction using our Markov chain model. An example simulation shows that correctly compensating for dead times in a high-flux measurement can yield a 20-times speed up of data acquisition. The resulting accuracy at high photon flux could enable real-time applications such as autonomous navigation

Estimation from quantized Gaussian measurements: when and how to use dither

Subtractive dither is a powerful method for removing the signal dependence of quantization noise for coarsely quantized signals. However, estimation from dithered measurements often naively applies the sample mean or midrange, even when the total noise is not well described with a Gaussian or uniform distribution. We show that the generalized Gaussian distribution approximately describes subtractively dithered, quantized samples of a Gaussian signal. Furthermore, a generalized Gaussian fit leads to simple estimators based on order statistics that match the performance of more complicated maximum likelihood estimators requiring iterative solvers. The order statistics-based estimators outperform both the sample mean and midrange for nontrivial sums of Gaussian and uniform noise. Additional analysis of the generalized Gaussian approximation yields rules of thumb for determining when and how to apply dither to quantized measurements. Specifically, we find subtractive dither to be beneficial when the ratio between the Gaussian standard deviation and quantization interval length is roughly less than one-third. When that ratio is also greater than 0.822/K^0.930 for the number of measurements K > 20, estimators we present are more efficient than the midrange.https://arxiv.org/abs/1811.06856Accepted manuscrip

Dead Time Compensation for High-Flux Ranging

Dead time effects have been considered a major limitation for fast data acquisition in various time-correlated single photon counting applications, since a commonly adopted approach for dead time mitigation is to operate in the low-flux regime where dead time effects can be ignored. Through the application of lidar ranging, this work explores the empirical distribution of detection times in the presence of dead time and demonstrates that an accurate statistical model can result in reduced ranging error with shorter data acquisition time when operating in the high-flux regime. Specifically, we show that the empirical distribution of detection times converges to the stationary distribution of a Markov chain. Depth estimation can then be performed by passing the empirical distribution through a filter matched to the stationary distribution. Moreover, based on the Markov chain model, we formulate the recovery of arrival distribution from detection distribution as a nonlinear inverse problem and solve it via provably convergent mathematical optimization. By comparing per-detection Fisher information for depth estimation from high- and low-flux detection time distributions, we provide an analytical basis for possible improvement of ranging performance resulting from the presence of dead time. Finally, we demonstrate the effectiveness of our formulation and algorithm via simulations of lidar ranging.Comment: Revision with added estimation results, references, and figures, and modified appendice

Analysis of the variation of the element types of properties and functions of technical systems in product development practice

In product development practice, it appears that engineering activities very often focus on the variation of the physical embodiment, as this is where the greatest and most obvious implications for the product seem to be perceived. Nevertheless, an empirical study revealed that variation in physical embodiment affects many other dimensions of a product, such as properties and functions. Within the scope of product specification, this requires a stronger differentiation of various dimensions of system elements. For this purpose, initial challenges and solution approaches in automotive product development practice are analyzed to gain a deeper understanding of the interrelationships of the variation of different types of system elements. The gathered findings and insights are then synthesized in a comprehensive systematic consisting of the structuring of elements of a new product generation or the reference system and an understanding of the set of elements in the Model of PGE – Product Generation Engineering. In summary, the differentiation of the variation types of the element types “property” and “function” is confirmed via the conducted case study. Further research should focus on supporting the product developer in identifying the alterations of the system elements by deriving the generic variation operator specifically onto the system elements of properties and functions of technical systems

Genomic expression dominance in allopolyploids

<p>Abstract</p> <p>Background</p> <p>Allopolyploid speciation requires rapid evolutionary reconciliation of two diverged genomes and gene regulatory networks. Here we describe global patterns of gene expression accompanying genomic merger and doubling in inter-specific crosses in the cotton genus (<it>Gossypium </it>L.).</p> <p>Results</p> <p>Employing a micro-array platform designed against 40,430 unigenes, we assayed gene expression in two sets of parental diploids and their colchicine-doubled allopolyploid derivatives. Up to half of all genes were differentially expressed among diploids, a striking level of expression evolution among congeners. In the allopolyploids, most genes were expressed at mid-parent levels, but this was achieved via a phenomenon of genome-wide expression dominance, whereby gene expression was either up- or down-regulated to the level of one of the two parents, independent of the magnitude of gene expression. This massive expression dominance was approximately equal with respect to direction (up- or down-regulation), and the same diploid parent could be either the dominant or the recessive genome depending on the specific genomic combination. Transgressive up- and down-regulation were also common in the allopolyploids, both for genes equivalently or differentially expressed between the parents.</p> <p>Conclusion</p> <p>Our data provide novel insights into the architecture of gene expression in the allopolyploid nucleus, raise questions regarding the responsible underlying mechanisms of genome dominance, and provide clues into the enigma of the evolutionary prevalence of allopolyploids.</p

Understanding the variation of physical elements and their impact on properties and functions: a case study on roll stabilization systems

This paper explores the variation in physical elements, functions, and properties of roll stabilization systems in automobiles over successive generations. Two key methodologies, Characteristics-Properties Modelling (CPM) / Property-Driven Development/Design (PDD) and the C&C²-Approach (Contact and Channel Approach), are utilized to analyze the attributes of the system elements and their functional correlations. Through detailed comparison of traditional roll stabilization subsystems and the active roll stabilization system, the research uncovers several correlations between variation types and system properties. The findings show the importance of attribute variation for understanding complex mechatronic systems. The research results may guide future planning of new product generations and foster innovative solutions in the early phases of product development

Dithered depth imaging

Single-photon lidar (SPL) is a promising technology for depth measurement at long range or from weak reflectors because of the sensitivity to extremely low light levels. However, constraints on the timing resolution of existing arrays of single-photon avalanche diode (SPAD) detectors limit the precision of resulting depth estimates. In this work, we describe an implementation of subtractively-dithered SPL that can recover high-resolution depth estimates despite the coarse resolution of the detector. Subtractively-dithered measurement is achieved by adding programmable delays into the photon timing circuitry that introduce relative time shifts between the illumination and detection that are shorter than the time bin duration. Careful modeling of the temporal instrument response function leads to an estimator that outperforms the sample mean and results in depth estimates with up to 13 times lower root mean-squared error than if dither were not used. The simple implementation and estimation suggest that globally dithered SPAD arrays could be used for high spatial- and temporal-resolution depth sensing.https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-28-23-35143Published versio